Asia Pacific Mathematics Newsletter Tributes to Solomon W Golomb

Rochelle Kronzek

s the measure of a man his intellect and all that he accomplishes during his lifetime or in how he treats his fellow human beings and those less fortunate or Iwith less opportunities? Sol Golomb was a polymath and a man of humility and integrity.

May 1, 2016 marked the passing of a brilliant, accomplished applied mathematician and the kindest of souls - Dr. Solomon Wolf Golomb, Distinguished Professor of Mathematics and at the University of Southern California (USC) where he had been an active member of the faculty for more than fifty years. He specialised in combinatorial analysis, number theory, coding theory and communications and became famous for the mathematical puzzles and games he created (including Polyominos which inspired the game Tetris). Dr. Golomb had accumulated many such honours and Only ten days prior to his passing, Dr. Golomb had been awards during his career including the National Medal of awarded the prestigious Franklin Medal 2016 in Electrical Science given by former US President Barack Obama in 2011. Engineering for his revolutionary work on shift register I first met Dr. Golomb in March 2010 during a sequences and their applications to space communications, Gathering for Gardner recreational mathematics satellite communications and cellular communications. Conference held in Atlanta. I was walking down a busy Marie Curie, Thomas Edison, Nikola Tesla, Bill Gates, downtown street returning to the conference hotel from Albert Einstein and Stephen Hawking are but a few of the lunch and found Dr. Golomb kneeling outside giving a visionaries whose work has been honoured by the homeless person the hot lunch he had purchased for them organisation previously. from a nearby restaurant.

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Solomon Wolf Golomb similarly walked across the Solomon W Golomb and Sequence Design at Tributes to Solomon W Golomb USC campus, greeting many students and colleagues along SWJTU. the way each day for the more than five decades that he 5. Vijay Kumar (video talk), IISC, India, Some Facets was a beloved professor. of Sol Golomb. Before USC, Sol conducted and supervised research Rochelle Kronzek 6. Guang Gong, University of Waterloo, Canada, in communications at the Caltech/NASA Jet Propulsion Golomb’s Shift Register Sequences for Wireless Laboratory (JPL) from 1956 through 1963 during the Communication, Cryptography and Radar — Work dawn of the Space Age. He went on to author or coauthor with a Great Mind. more than 200 journal articles and seven books and was particularly well known for his On January 31st, a day-long event entitled “The Life & pioneering and extensive work Legacy of Sol Golomb” celebrated Professor Golomb’s since 1953 on Shift Register great contributions to the electrical engineering Sequences and their appli- department, the University of Southern California (USC) cations to cryptography, radar and the campus Hillel. & coded, spread-spectrum The morning portion was held in the Viterbi School and wireless communications. of Engineering within department of electrical engineering Originally published in 1967, that Sol called home for more than five decades. World Scientific has produced Dr. Andrew Viterbi, a longtime friend of Dr. Golomb a reprint of this classic work attended and spoke at the memorial event. Viterbi, co- © 2017. founder of Inc. and the namesake for the Viterbi School of Engineering at USC met Golomb on his Several tributes were held in Dr. Golomb’s honour very first day at JPL, in 1957. Together they worked on during the latter half of 2016 and in 2017. NASA’s earliest satellite programs. SEquences and Their Applications (SETA) is the leading “My friendship with Sol lasted nearly six decades, international conference in the areas of sequences and during which time he grew from the brightest kid in the their applications to communication and cryptography. room to the wisest man on campus,” said Viterbi. It has been held in various locations around the world Several of Dr. Golomb’s former PhD students and starting on 1998 biannually. frequent research collaborators attended the USC A special feature of SETA 2016, which was held in symposium. Colleagues flew in from Norway, Canada, Chengdu (October 9–14, 2016), China, was a memorial India, Korea and Israel to participate. Albums and posters session in honour of Solomon W. Golomb. This event was containing pictures of Dr. Golomb were shared by his two held on October 10. Drs. Gong and Helleseth were the daughters Beatrice and Astrid. organisers for this event and there are six invited speakers After the morning symposium, the attendees then in this event, each gives a 50-minute talk for sharing their gathered in the Hughes Aircraft Electrical Engineering experience about their working or inspired by Dr. Golomb. Center lobby, where Dean Yannis Yortsos spoke and a bronze relief of Golomb was unveiled. The featured speakers for the SETA memorial and their talks were as follows:

1. Tor Helleseth, University of Bergen, Norway, Cross- correlation of Sequences and Golomb’s Norwegian Connection. 2. Steven Wolfram (video talk), Mathematica, GB, Cellular Automata and Shift Registers, or How Sol Golomb Almost Made My Favourite Discovery Before I Was Born. 3. Songyeop Song, Yonsei University, Korea, Prof. Golomb was my Advisor. 4. Pingzhi Fan, Southwest Jiao Tong University, China,

December 2017, Volume 7 No 1 33 Asia Pacific Mathematics Newsletter

Being the granddaughter of a rabbi myself, I appreciate 3) Hong-Yeop Song (Korea), “Existence of cyclic that Dr. Golomb was both the son and grandson of rabbis. Hadamard difference sets and some memories of A portion of the afternoon’s memorial service was given Prof. SW. Golomb”; and Grab this book at an exclusive % discount! by the campus Hillel rabbi, Hebrew songs were sung by 4) Andrew Viterbi (USA), “Celebrating the Life of 30 children and Bailey London, Executive Director of USC Solomon Wolf Golomb”. Quote WSSHIFTREGISTER30 at our online store to enjoy the discount. Hillel also paid tribute to Dr Golomb. The office of the President of USC co-sponsored the afternoon tribute and That evening an interactive puzzle session (with prizes)

held a private reception in Dr. Golomb’s honour. in Sol’s honour was also held, organised by Joe Buhler, Solomon W. Golomb by UC San Diego’s Information Theory and Applications Paul Cuff, Al Hales and Richard Stong. (University of Southern California, USA) (ITA) Center, at its 2017 Workshop in February, devoted Dr. Golomb will be missed but his legacy lives through an afternoon memorial session to “Remembering Sol his 50 years of teaching at USC, how he revolutionised Golomb”. It was organised by Tuvi Etzion (Israel), with digital communications with his book on shift register the following speakers: sequences and his kindness that touched me deeply after 1) Guang Gong (Canada), “Golomb’s Invariants and being with him just a handful of times. I was honoured Modern Cryptology”; to have been his editor. 2) Tor Helleseth (Norway), “Shift Register Sequences and Golomb’s Norwegian Connections”;

“Solomon Golomb’s classic book Shift Register Sequences… content lives on in pretty much every modern communications system. Read the specifications for 3G, LTE, Wi-Fi, Bluetooth, or for that matter GPS, and you’ll find mentions of polynomials that determine the shift register sequences these systems use Rochelle Kronzek to encode the data they send. Solomon Golomb is the person Rochelle Kronzek is Executive Editor for World Scientific based in who figured out how to construct these polynomials.” the . Dr Stephen Wolfram, Founder & CEO of Wolfram Research, Creator of Mathematica, Wolfram Alpha and the Wolfram Language

272pp Feb 2017 978-981-4632-00-3 US$118 / £98 978-981-4632-01-0(ebook) US$177 / £147 Order your copy at http://www.worldscientific.com/worldscibooks/10.1142/9361

Key Features: Shift register sequences cover a broad range of applications, from radar signal design, pseudo-random number generation, digital wireless • This is the third, revised edition of the telephony, and many other areas in coded communications. It is the primary definitive book on the subject area for which the author, Dr Golomb, received the US National Medal of Science. This book is the third, revised edition of the original definitive • Rigorous mathematical proofs are book on shift register sequences which was published in 1967, which has provided been widely distributed, read, and cited. It has stood the test of time, and • It is written in a way that is easy to provides a clear, comprehensive, and readily applicable description of both understand linear and non-linear shift register sequences.

Contents: Perspective: The Present Status of the Shift Register Art; The Shift Register as a Finite State Machine; The Linear Theory: Sequences Readership: Graduate students and researchers with Randomness Properties; Structural Properties of PN Sequences; working on communications, radar signal design, On the Factorization of Trinomials Over GF(2); The Nonlinear Theory: pseudorandom number generator, digital wireless Nonlinear Shift Register Sequences; Cycles from Nonlinear Shift Registers; telephony, and many other areas which require On the Classification of Boolean Functions. understanding of shift register sequences. 34 December 2017, Volume 7 No 1

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